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Unformatted text preview: MMAE 350 D. Rempfer Problem Set VII Page 1 of 2 Due Date: November 20, 2006 1. We want to investigate the dynamics of the simple swinging pendulum (see picture), which is thought of as a point mass that is suspended on a rod of zero mass and length l , in a gravitational field with an acceleration of g . The angle between the vertical coordinate and the pendulum is denoted by . a. Use Newtons second law to derive the di ff erential equation that de- scribes the change of the angle with time. b. Linearize the nonlinear di ff erential equation you have obtained above. (Hint: Use a Taylor-series expansion for the function on the right-hand side of your di ff erential equation.) Q m l c. What is the exact solution of the linearized di ff erential equation, for ( t = 0) = 4 / 5, d /dt ( t = 0) = 0? d. Using Heuns predictor-corrector method, solve the exact di ff erential equation from part a. of this problem numerically, for the initial condition ( t = 0) = 4 / 5, d /dt ( t = 0) = 0, using g/ (2 ` ) = 1. Try to integrate over a time of t e = 4 , using step sizes h 1...
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This note was uploaded on 05/04/2008 for the course MMAE 350 taught by Professor Rempher during the Spring '05 term at Illinois Tech.
- Spring '05